Finite Group Databasebeta

← #18006392

Subgroups — #18006392

Order 4736.

476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558337C212yesmaximal, complemented
2#14558336C212yesmaximal, complemented
3#14557909C211yesmaximal, characteristic, complemented
4#14557802C212yesmaximal, complemented
5#14557801C212yesmaximal, complemented
6#14557702C212yesmaximal, complemented
7#14557700C211yesmaximal, characteristic, complemented
8#14557647C212yesmaximal, complemented
9C37×#453C211yesmaximal, characteristic, complemented
10#11924582C2212yescomplemented
11#11924581C2211yescharacteristic, complemented
12#11924564C2212yescomplemented
13#11924563—22no—
14#11924562—22no—
15#11924562C2212yescomplemented
16#11924561—22no—
17#11924561C2212yescomplemented
18#11924560—22no—
19#11924557—22no—
20#11924556—22no—
21#11924556C2212yes—
22C2×#10596939—22no—
23C2×#10596939C2212yescomplemented
24C2×#10596939C2212yescomplemented
25D8×D37—22no—
26#11924544C2212yescomplemented
27#11924543C2212yescomplemented
28#11924533C2211yescharacteristic, complemented
29#11924471C2212yescomplemented
30#11924464C2212yescomplemented
31#11924453C2211yescharacteristic, complemented
32#11924452C2212yescomplemented
33C4×#64436C2211yescharacteristic, complemented
34H(5,𝔽2)×C37C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C37C2212yescomplemented
36#127×C37C2211yescharacteristic, complemented
37#104×C37C2212yescomplemented
38#100×C37C2211yescharacteristic, complemented
39#41×C37—22no—
40#41×C37C2312yes—
41C2×D4×C37—22no—
42C2×D4×C37—41no—
43C2×D4×C37—41no—
44C2×D4×C37C2311yescharacteristic
45C2×D4×C37C2311yescharacteristic
46C2×C22⋊D37—41no—
47#10596966—22no—
48#10596964—22no—
49D4×D37—22no—
50D4×D37—22no—
51D4×D37—42no—
52#10596962—22no—
53#10596962C2312yes—
54C2×D148—22no—
55C2×D148—41no—
56C2×D148C2312yes—
57SD16×C37—22no—
58D8×C37—22no—
59M16×C37C2312yes—
60C42×C37C2311yescharacteristic
61#10596942D412yescomplemented
62#10596941—22no—
63#10596941D412yescomplemented
64#10596940—22no—
65#10596940D412yescomplemented
66#10596939—22no—
67#10596939—22no—
68#10596939—22no—
69#10596939—22no—
70#10596939—22no—
71#10596939—22no—
72#10596939D412yescomplemented
73#10596934—22no—
74#10596934C2312yes—
75C2×#64436—22no—
76C2×#64436C2312yes—
77D296—22no—
78#10596930—22no—
79#10596929—22no—
80C8×D37—22no—
81C23×C37—21no—
82C23×C37—21no—
83C23×C37—41no—
84C22×D37—22no—
85C22×D37—41no—
86C22×D37—42no—
87Q8×C37C2×D412yes—
88D4×C37—22no—
89D4×C37—22no—
90D4×C37—22no—
91D4×C37—42no—
92D4×C37—82no—
93D4×C37C2×D412yes—
94C2×C4×C37—21no—
95C2×C4×C37—22no—
96C2×C4×C37—41no—
97C2×C4×C37C2411yescharacteristic
98C22⋊D37—22no—
99C22⋊D37—42no—
100C22⋊D37—42no—
101C2×Dic37—41no—
102D148—22no—
103D148—22no—
104D148—42no—
105D148—82no—
106D148C2×D412yes—
107C4×D37—22no—
108C4×D37—42no—
109Dic74C2×D412yes—
110C8×C37—22no—
111#64436—22no—
112#64436C2×D412yes—
113#64436C2×D412yes—
114C22×C37—22no—
115C22×C37—41no—
116C22×C37—41no—
117C22×C37—81no—
118C22×C37—81no—
119C22×C37—161no—
120C22×C37H(5,𝔽2)11yescharacteristic
121C2×D37—22no—
122C2×D37—42no—
123C2×D37—82no—
124C2×D37—161no—
125C2×D37—162no—
126C4×C37—22no—
127C4×C37—22no—
128C4×C37C22×D412yes—
129Dic37—22no—
130#3292—371nomaximal, Sylow
131C2×C37—21no—
132C2×C37—42no—
133C2×C37—81no—
134C2×C37—81no—
135C2×C37D4211yescharacteristic
136D37—42no—
137D37—82no—
138#576—372no—
139#576—372no—
140#493—371no—
141#472—372no—
142#472—372no—
143#453—371no—
144#453—372no—
145#453D3711yescharacteristic, complemented
146#443—372no—
147C37#329211yescharacteristic, complemented, Sylow
148H(5,𝔽2)—372no—
149H(5,𝔽2)—371no—
150H(5,𝔽2)C2×D3711yescharacteristic, complemented
151AGL(1,ℤ/8)—372no—
152AGL(1,ℤ/8)—372no—
153AGL(1,ℤ/8)—372no—
154AGL(1,ℤ/8)—742no—
155AGL(1,ℤ/8)—742no—
156AGL(1,ℤ/8)—742no—
157AGL(1,ℤ/8)—742no—
158AGL(1,ℤ/8)C2×D3712yescomplemented
159#135—372no—
160#135—742no—
161#135—742no—
162C2×D8—372no—
163C2×D8—372no—
164C2×D8—742no—
165C2×D8—742no—
166#131—372no—
167#131—372no—
168#127—371no—
169#127C2×D3711yescharacteristic, complemented
170#108—372no—
171#104—372no—
172#104C2×D3712yescomplemented
173#100—371no—
174#100—372no—
175#100C2×D3711yescharacteristic, complemented
176C4×C8—371no—
177#41—22no—
178#41—372no—
179#41—742no—
180#41—742no—
181#41—742no—
182#41C22×D3712yes—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—372no—
187C2×D4—742no—
188C2×D4—742no—
189C2×D4—742no—
190C2×D4—1481no—
191C2×D4—1482no—
192C2×D4—1481no—
193C2×D4C22×D3711yescharacteristic
194C2×D4C22×D3711yescharacteristic
195Q16—372no—
196SD16—22no—
197SD16—372no—
198SD16—372no—
199SD16—742no—
200SD16—742no—
201SD16—742no—
202D8—22no—
203D8—372no—
204D8—742no—
205D8—742no—
206D8—742no—
207D8—742no—
208D8—742no—
209D8—742no—
210D8—742no—
211M16—372no—
212M16—742no—
213M16—742no—
214M16C22×D3712yes—
215C2×C8—372no—
216C2×C8—742no—
217C2×C8—742no—
218C42C22×D3711yescharacteristic
219C23—21no—
220C23—21no—
221C23—41no—
222C23—742no—
223C23—1482no—
224C23—1481no—
225Q8—372no—
226Q8D4×D3712yes—
227D4—22no—
228D4—22no—
229D4—22no—
230D4—42no—
231D4—82no—
232D4—372no—
233D4—2962no—
234D4—742no—
235D4—742no—
236D4—742no—
237D4—1482no—
238D4—1482no—
239D4—1482no—
240D4D4×D3712yes—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—742no—
245C2×C4—1482no—
246C2×C4—1481no—
247C2×C4C23×D3711yescharacteristic
248C8—22no—
249C8—372no—
250C8—372no—
251C8—742no—
252C22—22no—
253C22—41no—
254C22—41no—
255C22—81no—
256C22—81no—
257C22—161no—
258C22—2962no—
259C22—742no—
260C22—5922no—
261C22—5921no—
262C22—1482no—
263C22#1192458111yescharacteristic
264C4—22no—
265C4—22no—
266C4—742no—
267C4C2×D4×D3712yes—
268C2—21no—
269C2—42no—
270C2—81no—
271C2—81no—
272C2—2962no—
273C2—1482no—
274C2#1455816511yescharacteristic
subgroupG/H
centerC2#14558165
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#453C2
socleC2×C37D42
hypercenter#453D37
hypocenterC37#3292
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14558337C2semidirect
2. #14558336C2semidirect
3. #14557909C2semidirect
4. #14557802C2semidirect
5. #14557801C2semidirect
6. #14557702C2semidirect
7. #14557700C2semidirect
8. #14557647C2semidirect
9. C37×#453C2semidirect
10. #11924582C22semidirect
11. #11924581C22semidirect
12. #11924564C22semidirect
15. #11924562C22semidirect
17. #11924561C22semidirect
23. C2×#10596939C22semidirect
24. C2×#10596939C22semidirect
26. #11924544C22semidirect
27. #11924543C22semidirect
28. #11924533C22semidirect
29. #11924471C22semidirect
30. #11924464C22semidirect
31. #11924453C22semidirect
32. #11924452C22semidirect
33. C4×#64436C22semidirect
34. H(5,𝔽2)×C37C22semidirect
35. AGL(1,ℤ/8)×C37C22semidirect
36. #127×C37C22semidirect
37. #104×C37C22semidirect
38. #100×C37C22semidirect
61. #10596942D4semidirect
63. #10596941D4semidirect
65. #10596940D4semidirect
72. #10596939D4semidirect
145. #453D37semidirect
147. C37#3292semidirect
150. H(5,𝔽2)C2×D37semidirect
158. AGL(1,ℤ/8)C2×D37semidirect
169. #127C2×D37semidirect
172. #104C2×D37semidirect
175. #100C2×D37semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145583372
#145583362
#145579092
#145578022
#145578012
#145577022
#145577002
#145576472
C37×#4532
#329237